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Assessment of Local Influence in GARCH Processes

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  • Xibin Zhang

Abstract

. This paper investigates the problem of assessing local influence of small perturbations in GARCH processes. First, we examine the local influence on the Lagrange multiplier (LM) statistic. Second, we assess the local influence on the pseudo‐likelihood of the GARCH model. We find that short patches of high volatility observations that have a strong influence on the LM statistic may not necessarily be influential on the pseudo‐likelihood. This is mainly due to the fact that the effects of high volatility could be incorporated through GARCH modeling. An empirical example is presented to illustrate the effectiveness of the proposed methods. It is interesting to note that observations which have a very strong influence on the LM statistic are far less influential on the GARCH pseudo‐likelihood, suggesting that under the GARCH model they should not be regarded as outliers.

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  • Xibin Zhang, 2004. "Assessment of Local Influence in GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 301-313, March.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:2:p:301-313
    DOI: 10.1046/j.0143-9782.2003.00351.x
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    1. Lee, John H H & King, Maxwell L, 1993. "A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 17-27, January.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    4. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    1. Lei Shi & Md. Mostafizur Rahman & Wen Gan & Jianhua Zhao, 2015. "Stepwise local influence in generalized autoregressive conditional heteroskedasticity models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 428-444, February.
    2. L. Grossi & G. Morelli, 2006. "Robust volatility forecasts and model selection in financial time series," Economics Department Working Papers 2006-SE02, Department of Economics, Parma University (Italy).
    3. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2004. "Spurious And Hidden Volatility," Working Papers. Serie AD 2004-45, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Grossi, Luigi & Laurini, Fabrizio, 2009. "A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2251-2263, April.
    5. Jonathan Dark & Xibin Zhang & Nan Qu, 2010. "Influence diagnostics for multivariate GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 278-291, July.
    6. Grané, Aurea & Veiga, Helena, 2010. "Outliers in Garch models and the estimation of risk measures," DES - Working Papers. Statistics and Econometrics. WS ws100502, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Fukang Zhu & Lei Shi & Shuangzhe Liu, 2015. "Influence diagnostics in log-linear integer-valued GARCH models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 311-335, July.
    8. Xibin Zhang & Maxwell L. King, 2002. "Influence Diagnostics in GARCH Processes," Monash Econometrics and Business Statistics Working Papers 19/02, Monash University, Department of Econometrics and Business Statistics.
    9. Grané, Aurea & Veiga, Helena, 2010. "Wavelet-based detection of outliers in financial time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2580-2593, November.

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